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Math 1113 Pre-Calculus Quiz 3 Practice Summer 2008
Name: Last ___________________, First ______________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the exact value of the expression.
- tan
A)
2 π
B)
π
C)
π
D)
5 π
- cos
A)
π
B)
5 π
C)
2π
D) -
3π
- sin
A)
π
B)
7 π
C)
π
D)
7 π
Use a calculator to find the value of the expression rounded to two decimal places.
- sin
A) 1.32 B) 14.48 C) 0.25 D) 75.
- cos
A) 55.15 B) 34.85 C) 0.61 D) 0.
Find the exact value, if any, of the composite function. If there is no value, say it is "not defined". Do not use a calculator.
- cos[cos
(-1.8)]
A) 1. 8 B) 0. 8 C) - 1. 8 D) not defined
- tan(tan
A) 1 B) 8 C) - 8 D) not defined
Find the inverse function f
of the function f.
- f(x) = - 6 cos(10x + 7 )
A) f
cos
x
(x) = - 6 cos
(10x + 7)
C) f
cos
x
cos
x
- f(x) = - sin(x + 4 ) - 2
A) f
(x) = sin
(x + 2) - 4 B) f
(x) = - sin
(x + 4) - 2
C) f
(x) = - sin
(x + 2) - 4 D) f
(x) = - sin
(x - 2) + 4
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
- When light travels from one medium to anotherfrom air to water, for instanceit changes
direction. (This is why a pencil, partially submerged in water, looks as though it is bent.)
The angle of incidence θr is the angle in the first medium; the angle of refraction θr is the
second medium. (See illustration.) Each medium has an index of refractionni and nr,
respectivelywhich can be found in tables. Snell's law relates these quantities in the
formula
ni sinθi = nr sin θr
Solving for θr, we obtain
θr = sin
ni
nr
sin θi
Find θr for air (ni = 1.0003), methylene iodide (nr = 1.74), and θi = 14.7°.
Simplify the trigonometric expression by following the indicated direction.
- Factor and simplify:
2 sin
θ + 3 sin θ + 1
sin2 θ - 1
Establish the identity.
- tan θ · csc θ = sec θ 12)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Simplify the expression.
cos θ
1 + sin θ
tan θ
A) sin
θ B) 1 C) sec θ D) cos θ + sin θ
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Show that the functions f and g are identically equal.
- f(θ) = csc θ + cot θ, g(θ) =
sin θ
1 - cos θ
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
- A water wheel rotates through the angle θ, the water level L behind the wheel changes
according to the equation
L
sin θ
where L is measured in inches. Determine the values of θ for which the water level is zero.
Find the exact values. Do not use a calculator.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation on the interval 0 ≤ θ < 2 π.
- cos
θ - sin
θ = 1 + sin θ
A) 0,
π
5 π
, π B) 0, π,
4 π
5 π
C) 0, π,
7 π
11 π
D)
π
7 π
3π
11 π
- sin
θ = 5(cos θ + 1)
A) 0 B)
3π
C) π D) No solution
Solve the problem.
- An electric generator produces a 30-cycle alternating current described by the equation
I(t)
40 sin 60π t
where I(t) amperes is the current at t seconds. Find the smallest value of t for which the current is 20
amperes.
A)
B)
C)
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use a calculator to solve the equation. Round the solution(s) to two decimal places if necessary.
- x
3 sin(2x)
2x 27)
- e
x
cos x 28)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use a graphing utility to solve the equation on the interval 0° ≤ x < 360 °. Express the solution(s) rounded to one decimal
place.
- sin
x + 8 sin x - 4 = 0
A) 28.2°, 151.8° B) 208.2°, 331.8°
C) 28.2°, 151.8°, 208.2°, 331.8° D) No solution
- tan
x + 5 tan x + 3 = 0
A) 103.1°, 145.1°, 283.1°, 325.1° B) 70.5°, 109.5°, 180.0°
C) 51.8°, 128.2° D) 49.8°, 130.2°, 229.8°, 310.2°
Answer Key
Testname: MATH 1113 Q3-PRACTICE
1) B
2) B
3) C
4) C
5) D
6) D
7) B
8) C
9) C
- θ r
2 sin θ + 1
sin θ - 1
- tan θ · csc θ =
sin θ
cos θ
sin θ
cos θ
= sec θ
13) C
- g(θ) =
sin θ
1 - cos θ
sin θ
1 - cos θ
1 + cos θ
1 + cos θ
sin θ(1 + cos θ)
1 - cos2 θ
sin θ(1 + cos θ)
sin2 θ
1 + cos θ
sin θ
sin θ
cos θ
sin θ
= csc θ + cot θ
= f(θ)
15) C
16) C
17) B
18) C
19) D
20) C
21) D
22) A
- θ =
π
7 π
11 π
24) C
25) C
26) D
29) A
30) A
